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On gradings of matrix algebras and descent theory

S. Caenepeel·S. Dăscălescu·C. Năstăsescu
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Abstract

We classify gradings on matrix algebras by a finite abelian group. A grading is called good if all elementary matrices are homogeneous. For cyclic groups, all gradings on a matrix algebra over an algebraically closed field are good. We can count the number of good gradings by a cyclic group. Using descent theory, we classify non-good gradings on a matrix algebra that become good after a base extension.

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S. Caenepeel, S. Dăscălescu, C. Năstăsescu. 2001-07-20. On gradings of matrix algebras and descent theory. https://arxiv.org/abs/math/0107148

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